Weird bouyancy/mass/density problem

[cubejunkies]

So I'm doing a summer homework assignment for AP Chem and I took normal honors chem last year so I know terminology and things like that, but this question in the summer homework assignment for AP Chem that I've been working on in the review-ish section of the book is not making any sense. I have no idea where to start with this problem. Even though its in a chem book, it seems like a physics question, however, which is why I am posting it here. The problem is as follows:

"A student is given a crucible and asked to prove whether it is made of pure platinum. She first weighs the crucible in air and then weighs it suspended in water (density = 0.9986 g/mL). The readings are 860.2 g and 820.2 g, respectively. Based on these measurements and given that the density of platinum is 21.45 g/cm^3, what should her conclusion be? (Hint: An object suspended in a fluid is bouyed up by the mass of the fluid displaced by the object. Neglect the bouyance of air.)"

Sorry if this is a really stupid question to ask and if the solution should be obvious

Anthony

 

[ehild]

Apply Archimedes' principle. How is the buoyant force related to the volume of the crucible and the density of water?

ehild

 

[cubejunkies]

I honestly have no idea :(

 

[ehild]

Read this:

http://en.wikipedia.org/wiki/Archimedes#The_Golden_Crown

Anyway: The apparent way of a submerged object is less the the real weight by the weight of the disclosed fluid.

ehild

 

[rwisz]

Hi Anthony,

Thank you for reaching out with your question. It's great to see you taking on challenging material and seeking help when needed.

To start, let's define some terms and equations that will help us solve this problem:

- Buoyancy: the upward force that a fluid exerts on an object that is partially or fully submerged in it
- Mass: a measure of the amount of matter in an object
- Density: the amount of mass per unit volume of a substance
- Archimedes' Principle: the buoyant force on an object is equal to the weight of the fluid that the object displaces

Now, let's apply these concepts to the problem at hand. The student is trying to determine if the crucible is made of pure platinum, which has a known density of 21.45 g/cm^3. To do this, she first weighs the crucible in air, which gives a reading of 860.2 g. This is the mass of the crucible and any air that is displaced by it.

Next, she weighs the crucible suspended in water, which gives a reading of 820.2 g. This means that the buoyant force of the water is acting on the crucible, reducing its apparent weight. We can use Archimedes' Principle to calculate the buoyant force:

Buoyant force = Weight of water displaced = (volume of water displaced) x (density of water) x (acceleration due to gravity)

To find the volume of water displaced, we can use the fact that the density of water is 0.9986 g/mL. So, the volume of water displaced is (860.2 g - 820.2 g)/(0.9986 g/mL) = 40 mL.

Plugging this into our equation for buoyant force, we get:

Buoyant force = (40 mL) x (0.9986 g/mL) x (9.8 m/s^2) = 392.7 g

This means that the buoyant force acting on the crucible is 392.7 g, which is the weight of the water displaced. Now, we can find the weight of the crucible itself by subtracting the buoyant force from the weight measured in air:

Weight of crucible = 860.2 g - 392.7 g = 467.5 g

Finally, we can use the density equation (density = mass/v